Question Video: Simplifying Quotients of Fractions Containing Monomials Mathematics

Consider the expression (3π‘₯³𝑦/5π‘₯𝑦)/(6π‘₯⁴/5𝑦⁴). It is often easier to rewrite the expression using the division symbol as follows: (3π‘₯³𝑦/5π‘₯𝑦) Γ· (6π‘₯⁴/5𝑦⁴). Then, we can rewrite the expression using the multiplication symbol: (3π‘₯³𝑦/5π‘₯𝑦) Γ— (5𝑦⁴/6π‘₯⁴). Now, use this form to help you simplify the original expression.

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Video Transcript

Consider the expression three π‘₯ cubed 𝑦 over five π‘₯𝑦 divided by six π‘₯ to the power of four over five 𝑦 to the power of four.

It is often easier to rewrite the expression using the division symbol as follows: three π‘₯ cubed 𝑦 divided by five π‘₯𝑦 divided by six π‘₯ to the power of four divided by five 𝑦 to the power of four. Then, we can rewrite the expression using the multiplication symbol: three π‘₯ cubed 𝑦 divided by five π‘₯𝑦 multiplied by five 𝑦 to the power of four divided by six π‘₯ to the power of four.

Now, use this form to help you simplify the original expression. There are two ways of approaching this problem. We could cancel or simplify first and then multiply the two fractions or we could multiply the two fractions and simplify this single fraction. We’re going to use the second method.

Multiplying the two numerators gives us 15π‘₯ cubed 𝑦 to the power of five as three π‘₯ cubed 𝑦 multiplied by five 𝑦 to the power of four is equal to 15π‘₯ cubed 𝑦 to the power of five. In the same way, multiplying the denominators, five π‘₯𝑦 multiplied by six π‘₯ to the power of four, gives us 30π‘₯ to the power of five 𝑦.

We can then cancel or simplify this expression. 15 divided by 30 is equal to a half. π‘₯ cubed divided by π‘₯ to the power of five leaves us π‘₯ squared on the denominator. And 𝑦 to the power of five divided by 𝑦 is 𝑦 to the power of four.

Therefore, the simplified expression is 𝑦 to the power of four divided by two π‘₯ squared. Rewriting the initial expression has made it easier to simplify.

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